Once I made and parented a rig, can I still add more bones? (forgot the tail)
Yes. An armature can be adjusted multiple times.

Armatures typically are parented with a default weight paint for organic creatures.  Next weight paint is used to refine your weights of bones.  Vertex groups are the typical mechanism for control.

So you have two options.


Preferred. Reuse. Use  the vertex groups you have and paint new vertex groups for the tail bones.  Expect some adjustments for previous bones near the tail bones.
More work if you choose to start from beginning. Delete the old armature modifier and all vertex groups and parent again to the armature.  Weight paint again.


Armature and their weights can come and go just like any other Blender Feature.  The first one can be challenging.  The works gets easier each new attempt at armature and weight painting.  You can archive your file for extra peace of mind.